LCD displays are frequently used for displaying information to a user, below called the viewer, of a mobile phone, a PDA or other electronic device. An LCD display is preferably illuminated with polarized light. The illumination could be made either as a back light illumination where the light is emitted towards the viewer via the display panel or as a front light illumination where the light is emitted towards the display panel and is then reflected back towards the viewer. The international application 97/08582 describes a display device including an optical waveguide for providing illumination of a display panel. The optical waveguide is provided with grooves that are filled with a birefringent material. The birefringent material in the grooves splits light incoming from the side into two light beams having mutually opposite polarization. The grooves of the optical waveguide are thus filled with an anisotropic uniaxial material, for example nematic liquid crystalline material, to achieve the outcoupling of polarized light of a desired polarization towards the display panel that is to be illuminated. The optical wave guide is however sensitive to the manufacturing steps and may, if the grooves do not obtain a high quality with respect to surface properties and filling, result in the outcoupling of a substantial amount of light of the not wanted polarization.